1. © 2002 QxDesign, Inc. Variation of plant gain This unit discusses Changes in system stability with increasing plant gain Adjusting KP to correct for changing plant gain Gain scheduling Visual ModelQ Training

2. © 2002 QxDesign, Inc. Install Visual ModelQ Click here to visit www.QxDesign.com **This unit can be completed with a free (unregistered) copy of Visual ModelQ Download Visual ModelQ** Run Visual ModelQ installation Launch Visual ModelQ using the Windows start button or clicking on the icon The “default model” should appear To run Visual ModelQ the first time:

3. © 2002 QxDesign, Inc. Start with the model “Building a PI Controller” Visit www.QxDesign.com/VisualModelQ#Training Download “Building a PI Controller.mqd” or build the model yourself using the presentation “Building a PI Controller.pps”

4. © 2002 QxDesign, Inc. Check performance with the initial values Click the run button to see the performance with the initial gains of KP = 100, KP = 2, and with a System Gain of 500. Looks good; feedback responds fast, with little overshoot. Command (blue) Feedback (red)

5. © 2002 QxDesign, Inc. What is plant gain? The plant in this model is an integral with a “System Gain” of 500. A single integrator with a gain is the most common plant in industrial controls: –Inductor in current supply …applied voltage integrates to current –Inertial load in motion control …applied torque (force) integrates to velocity –Temperature bath …applied heat integrates to temperature –Capacitance in a voltage supply …applied current integrates to voltage

6. © 2002 QxDesign, Inc. Why does plant gain vary? The plant gain often changes with time or operating conditions –Inductor in current supply …inductors saturate: inductance falls when current is high. –Inertial load in motion control …inertia changes with varying loads –Temperature bath …thermal mass varies when fluid level in the bath changes –Capacitance in a voltage supply … capacitance of electrolytic capacitors fall over time

7. © 2002 QxDesign, Inc. See how varying plant gain affects the system Double-click in System Gain for adjuster box. While the model runs, increase to 1000, 2000, and so on. Live Constant adjuster box allows easy adjustment of gains, even while the model runs.

8. © 2002 QxDesign, Inc. Gain = 500Gain = 1000Gain = 2000 What happens as gain increases? Increase the gain from 500 to 2000. The system becomes unstable as the gain increases. Slight ringing… questionable Severe ringing… not acceptable TIP: Use adjustment such as “>>” (large increase) to quickly vary gains while the model runs 10% Overshoot… looks good!

9. © 2002 QxDesign, Inc. What’s a practical example? Current controller with saturating inductor –PI control law generates a voltage request. –Request feeds “voltage controller” (e.g., power transistor). –Voltage controller produces applied voltage. –The “gain” of an inductor is 1/inductance. –Saturation reduces inductance as current increases...higher current causes higher gain. –Result: system can be stable with low current, but unstable at high current.

10. © 2002 QxDesign, Inc. KP = 2 Retuning can solve the problem When “System Gain” increases, reducing KP restores stability. With most PI controllers, if you reduce KP in proportion to gain increase, the problem is solved. Gain = 2000 Gain increases 4x; stability suffers. KP = 2 Gain = 2000 Lower KP 4x; problem solved. KP = 0.5 Gain = 500 At start, system looks good!

11. © 2002 QxDesign, Inc. Gain scheduling: when retuning is impractical. If the gain changes during operation (like an inductor), you can’t retune to fix the problem. The most common solution is to lower KP so the system is always stable. Problem: KP may be lowered so much that response is slow when “System gain” is low. Another solution is gain scheduling, a technique often implemented with digital controllers. With gain scheduling, the digital controller estimates the system gain and adjusts KP appropriately. –For the example of the saturating inductor, KP could be a function of current. KP 2.0 0.0 1.0 Current 0.0 1.0 A -1.0 A Gain scheduling: A digital controller can continuously adjust KP as Current changes

12. © 2002 QxDesign, Inc. Visit www.QxDesign.com for information about software and practical books on controls. Click here for information on Visual ModelQ Click here for information on Observers in Control Systems, published by Academic Press in 2002 Click here for information on Control System Design Guide (2nd Ed.), published by Academic Press in 2000